Directions: Using the digits 1 to 9, at most one time each, create an equation where x has a positive (or negative) value.

### Hint

What makes a solution positive (or negative)?

Where do you want to put the larger (or smaller) numbers?

Where do you want to put the larger (or smaller) numbers?

### Answer

There are many solutions that would work.

Example that would give a positive solution:

(1/2)(4x + 8) + 6x = 9x + 3 … here, x = 1

Example that would give a negative solutions

(1/3)(6x + 9) + 2x = 5x + 7 … here, x = -4

Another constraint or extension you could add is change the directions to say: “Use the digits 1 to 9, at most one time each, to create an equation where x has a positive (or negative) integer value.”

Source: Daniel Luevanos

(1/3)(6x+9)+2x=5x+7

x=-4

(1/2)(4x+8)+6x=9x+3

x=1

3/6(2x+4)+7x=6x+5

x= 1.5

2/6(4x+8)+7x=3x+9

x=1.2

1/3(4+8)+2x=2x+8

x=4

1/2(5x+6)+3x=4x+9

X=4

1/2(-9x(4)=8x(2)

(1/2)(4x + 8) + 6x = 9x + 3

which is 1

(1/2)(4x + 8) + 6x =9x + 3

which is 1

5/3 (6x+3+1x=4x+3

x=-0.28

3/4(8x+7)+3x=11x+2

1/2(4x-2)+3x=-2x+4

x=5

1/2x(2x-1)+4x=-6x+2

x=no solution

2/3x-1/6=1/2x+5/6

x=6

(1/2)(4x+8)+6x=9x+3

x=1

2/1(4x+6)+7x=5x+8

(1/2)(4x+9)+6x= 7x+2

1/2(5x+6)+3x=4x+9 X=4

1/5 (3x + 2) + 4x = 6x + 8

X=6

1/5 (3x + 2) + 4x = 6x + 8

X=6

3/4m−2(m−1)= 1/4m+5

m=-2

1/6(2x+3)+7x=-12+10

x=3

1/6(1x+9)+2x=4x+6

x=5

1/2 ( 4x + 8 ) -2 = 4x + 3

x = -1/2

1/2(4x+6)+5x=7x+3 which means x = 0